Fractional, Circular, and Defective Coloring of Series-Parallel Graphs

نویسندگان

  • Wayne Goddard
  • Honghai Xu
چکیده

In this note we consider colorings of series-parallel graphs. Specifically, we provide bounds on their fractional and circular chromatic numbers and the defective version of these parameters. The main result is that the fractional chromatic number of any series-parallel graph of odd girth k is exactly 2k/(k − 1).

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Defective circular coloring

The concept of a defective circular coloring is introduced, and results shown for planar, series-parallel, and outerplanar graphs. Numerous problems are also stated.

متن کامل

Fractional and circular 1-defective colorings of outerplanar graphs

A graph is called fractional ( r s , d ) -defective colorable if its vertices can be colored with r colors in such a way that each vertex receives s distinct colors and has at most d defects (a defect corresponds to the situation when two adjacent vertices are assigned with non-disjoint sets). We show that each outerplanar graph having no triangle faces sharing a vertex is fractional ( 7 3 , 1 ...

متن کامل

Bounds on circular consecutive choosability

The circular consecutive choosability chcc(G) of a graph G has been recently introduced in [2]. In this paper we prove upper bounds on chcc for series-parallel graphs, planar graphs and k-choosable graphs. Our bounds are tight for classes of series-parallel graphs and k-choosable graphs for k ≥ 3. Then we study the circular consecutive choosability of generalized theta graphs. Lower bounds for ...

متن کامل

The circular chromatic number of series-parallel graphs of large odd girth

In this paper, we consider the circular chromatic number c (G) of series-parallel graphs G. It is well known that series-parallel graphs have chromatic number at most 3. Hence their circular chromatic number is also at most 3. If a series-parallel graph G contains a triangle , then both the chromatic number and the circular chromatic number of G are indeed equal to 3. We shall show that if a se...

متن کامل

Circular Chromatic Number of Hypergraphs

The concept of circular chromatic number of graphs was introduced by Vince(1988). In this paper we define circular chromatic number of uniform hypergraphs and study their basic properties. We study the relationship between circular chromatic number with chromatic number and fractional chromatic number of uniform hypergraphs.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Journal of Graph Theory

دوره 81  شماره 

صفحات  -

تاریخ انتشار 2016